I do this exclusively now.
I got the idea by reading through the example of "how to roleplay" in the Moldvay (1981) D&D basic set. The DM was the only one with a set of dice, and he rolled all the attack and damage rolls, even the players'. I thought that this was very unusual and would place a tremendous burden on the DM.
Then I actually tried it out... and it rocked. With no "toys" at the table to distract and fidget with, the players actually had nothing to focus on except imagining what their characters would do, given the current situation.
Nowadays, I prefer the "blind" method across the board. When I DM the game, I roll all the dice, and I keep all of the players' numerical statistics hidden from them, with the sole exception of Movement rate (that being the only statistic with a numerical value that the characters themselves could conceivably be aware of). In short, the players only know what their characters know: Fred the Fighter has High Strength, Above Average Constitution, Average Dexterity and Intelligence and Wisdom, and Below Average Charisma. At the moment, he's Not Wounded. His experience level goes from Veteran to Warrior to Swordmaster to Hero to Swashbuckler, etc., etc. The character certainly doesn't know what his THAC0 or his Save vs. Death Ray might be, so those numbers are hidden safely behind my DM's screen.
It heightens the immersion and pretty much stunts all meta-gaming. This is a very good thing in a role-playing game (although I can see why one wouldn't like it very much in a miniatures skirmish game).